Ethnographic research highlights that there are constraints placed on the time available to produce cultural artefacts in differing circumstances. Given that copying error, or cultural ‘mutation’, can have important implications for the evolutionary processes involved in material culture change, it is essential to explore empirically how such ‘time constraints’ affect patterns of artefactual variation. Here, we report an experiment that systematically tests whether, and how, varying time constraints affect shape copying error rates. A total of 90 participants copied the shape of a 3D ‘target handaxe form’ using a standardized foam block and a plastic knife. Three distinct ‘time conditions’ were examined, whereupon participants had either 20, 15, or 10 minutes to complete the task. One aim of this study was to determine whether reducing production time produced a proportional increase in copy error rates across all conditions, or whether the concept of a task specific ‘threshold’ might be a more appropriate manner to model the effect of time budgets on copy-error rates. We found that mean levels of shape copying error increased when production time was reduced. However, there were no statistically significant differences between the 20 minute and 15 minute conditions. Significant differences were only obtained between conditions when production time was reduced to 10 minutes. Hence, our results more strongly support the hypothesis that the effects of time constraints on copying error are best modelled according to a ‘threshold’ effect, below which mutation rates increase more markedly. Our results also suggest that ‘time budgets’ available in the past will have generated varying patterns of shape variation, potentially affecting spatial and temporal trends seen in the archaeological record. Hence, ‘time-budgeting’ factors need to be given greater consideration in evolutionary models of material culture change.